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Characters' heights, Unit MA and Unit Cm
Part A: Relative height = Misc. Constants In the geometric facts article, we explained the construction of the "coin" which shows in Ep. 36 ~ Ep.48. Now we generalize it: Let the Inner and the Outer ( of the construction circle ) be b and a, the middle red as K*a, the middle green as (1/K)*b. ( in the "coin"'s case, K=2/3 ). The angle as Theta. Then the sum of the coin-shape area is: a\cdot b\cdot \left( \dfrac {1} {k}-k\right) \cdot \sin \dfrac {\theta } {2} This formula is much simpler then other shapes ( which constructed by these 4 circles ). If we calculate the ratio between the "coin area" and the outer circle, we have: ( let the ratio be x ) x=\dfrac {a\cdot\pi } {b\cdot\left( \dfrac {1} {k}-k\right)\cdot \sin \left( \dfrac {\theta } {2}\right) } Let Theta = 360 / v , we know it has: \lim _{v\rightarrow \infty }v \cdot \sin \left( \dfrac {\pi } {v}\right) =\pi So x is roughly ( 99.715~% when v = 24 ) : x=\dfrac {a\cdot v} {b\cdot\left( \dfrac {1} {k}-k\right) } Now we know, only when K = 0.618033~, the golden ratio, ''then x can be (a / b)*v. This is the relation between the golden ratio and this kind of "shape" ( not the coin itself ). We point out before that Magical Princess : Chacha is also 1 : 0.618~: That some supports that we claim the ''golden ratio ''as a "legit" constant in Akazukin Chacha. There are also some constants we will use: h = tan(360/7) = 1.25396034~ nearly 79/63 or (9^2-2)/(8^2-1) y = 365.242199 A maybe misprinted Mahoujin The Mahoujin formation shown on LD-13 ( DVD v2-6 ) conflict with other displays in many ways, like the heptagon is not a regular one, the white rims overlaps each other ... etc. Early "researchers" of Akazukin Chacha like こっべ did not count it as a well-displayed one. However we still can see many properties of the normal one in this maybe "misprinted" one, like the Outer : Inner : P ( the yellow heptagram's ) = sqrt(2) : 1 : sqrt(2)*cos(360/7) ratio. The rim and small circles may be just adjusted for better visual. dlok.jpg tumblr_o004rqDrY61uj01ngo9_r1_1280.jpg More we can see is, Magical Princess' arms are on the ( reversed ) heptagram, Chacha's feet touch the heptagon inside P circle. MP's height is as the diameter of the Outer Circle; Chacha's height is as the diameter of the inner deep green heptagram's circumcircle. ( That's said MP's is adjusted bigger of Chacha is adjusted smaller, and both are 2+ times lager then Ep.48,50's Mahoujin-Character ratio ) These are some reason we believe this formation still shows properties of Akazukin Chacha itself, although most are unclear by now. Despite of the geometric aspect, we can see MP and Chacha on LD13 cover can be linked with the ''Vitruvian Man Pose. ''In below we will see this ( the vitruvian-formation ) does exist in Akazukin Chacha itself. Vitruvian Man Formation and two supports of it The animation below show the construction of the "base circle" and the "base square" of ''Vitruvian Man Formation ( of course Leonardo's, since we focus on its "natural" or mathematical properties, from Leonardo da Vinci or whoever is irrelevant ) form heptagon. This was originally used to explain MP's ''"eidos / idea of human" ''role. We can see the relations between her body parts or costume with those lines. The thing we want to bring out from this formation is the "base circle", which is 2*0.618~ times of the height of MP. First, in Ep. 48, the "Inner" and "Outer" of the "mural Mahoujin" is same as the normal Mahoujin ( both are 1 : sqrt(2) ) as the pic below: And we know MP's height is equal to the radius of Inner. In below we align MP and the exaggerated-art-style Mural MP / Joan I , and we can see the top of the "base circle" of MP is just at the same horizont of the Mural one's head. ...editing...Category:Extras